The topological basis realization and the corresponding XXX spin chain

Sun, Chunfang; Xue, Ke; Wang, Gangcheng; Zhou, Chengcheng; Du, Guijiao

doi:10.1209/0295-5075/94/50001

Cited by 16 publications

(4 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The authors showed that the maximum of the L 1 −norm connectes with the maximally entangled states. It was to noting that the theory of topological basis provides an useful method to solve quantum spin chain models [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Topological basis associated with B–M–W algebra: Two-spin-1/2 realization

et al. 2015

View full text Add to dashboard Cite

In this letter, we study the two-spin-1/2 realization for the Birman-Murakami-Wenzl (B-M-W) algebra and the corresponding Yang-BaxterȒ(θ, φ) matrix. Based on the two-spin-1/2 realization for the B-M-W algebra, the three-dimensional topological space, which is spanned by topological basis, is investigated. By means of such topological basis realization, the four-dimensional Yang-BaxterȒ(θ, φ) can be reduced to Wigner D J function with J = 1. The entanglement and Berry phase in the spectral parameter space are also explored. The results show that one can obtain a set of entangled basis via Yang-BaxterȒ(θ, φ) matrix acting on the standard basis, and the entanglement degree is maximum when theȒ i (θ, φ) turns to the braiding operator.

show abstract

Section: Introductionmentioning

confidence: 99%

Topological basis associated with B–M–W algebra: Two-spin-1/2 realization

et al. 2015

View full text Add to dashboard Cite

show abstract

“…On the other hand, the topological basis theory was introduced to study a quantum spin chain model [39][40][41]. In ref.…”

mentioning

confidence: 99%

“…In ref. [41], the authors studied the Heisenberg XXX model via the topological basis approach. The results show that the topological basis space is equivalent to the spin singlet space, and for the antiferromagnetic Heisenberg XXX model, the ground state is one of the topological basis states.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Topological basis realization associated with Hermitian and non-Hermitian Heisenberg XXZ model

Gong

Wang

Sang

et al. 2018

EPL

View full text Add to dashboard Cite

We investigate the topological basis realization associated with the Hermitian and non-Hermitian Heisenberg XXZ model based on the matrix representation of the Temperley-Lieb algebra. The results show that the topological space is spanned by the topological basis associated with the Temperley-Lieb algebra. When the q-deformed parameter q is a complex number and |q| = 1, the corresponding model is the non-Hermitian XXZ model. The real q corresponds to the Hermitan case. The topological basis realization for these two cases is constructed by means of matrix representation of the Temperley-Lieb algebra. Then the properties of the topological basis and ground state are studied. Particularly, the four-qubit Heisenberg XXZ model is investigated in detail. We also give some discussions on the case in which q is a root of unity.

show abstract